<page>			   EXHIBIT 31.01
CERTIFICATIONS

I, Jeffrey A. Rothman, President of Demeter Management Corporation
(?Demeter?), the general partner of the registrant, Dean Witter
Cornerstone Fund III, certify that:

1.	I have reviewed this quarterly report on Form 10-Q of the
registrant;

2.	Based on my knowledge, this report does not contain any untrue
statement of a material fact or omit to state a material fact
necessary to make the statements made, in light of the
circumstances under which such statements were made, not
misleading with respect to the period covered by this  report.

3.	Based on my knowledge, the financial statements, and other
financial information included in this report, fairly present
in all material respects the financial condition, results of
operations and cash flows of the registrant as of, and for,
the periods presented in this report;

4.	The registrant?s other certifying officer and I are
responsible for establishing and maintaining disclosure
controls and procedures (as defined in Exchange Act Rules 13a-
15(e) and 15d-15(e)) and internal control over financial
reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-
15(f)) for the registrant and have:

	a) Designed such disclosure controls and procedures, or caused
such disclosure controls and procedures to be designed
under our supervision, to ensure that material information
relating to the registrant, including its consolidated
subsidiaries, is made known to us by others within those
entities, particularly during the period in which this
report is being prepared;

	b) Designed such internal control over financial reporting, or
caused such internal control over financial reporting to be
designed under our supervision, to provide reasonable
assurance regarding the reliability of financial reporting
and the preparation of financial statements for external
purposes in accordance with generally accepted accounting
principles;

	c) Evaluated the effectiveness of the registrant?s disclosure
controls and procedures and presented in this report our
conclusions about the effectiveness of the disclosure
controls and procedures, as of the end of the period
covered by this report based on such evaluation; and


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	d) Disclosed in this report any change in the registrant?s
internal control over financial reporting that occurred
during the registrant?s most recent fiscal quarter (the
registrant?s fourth fiscal quarter in the case of an annual
report) that has materially affected, or is reasonably
likely to materially affect, the registrant?s internal
control over financial reporting; and

5.	The registrant?s other certifying officer and I have
disclosed, based on our most recent evaluation of internal
control over financial reporting, to the registrant?s
auditors and the audit committee of Demeter?s board of
directors (or persons performing the equivalent functions):

   a)	 All significant deficiencies and material weaknesses in the
design or operation of internal control over financial
reporting which are reasonably likely to adversely affect the
registrant?s ability to record, process, summarize and report
financial information; and

   b)	 Any fraud, whether or not material, that involves management
or other employees who have a significant role in the
registrant?s internal control over financial reporting.






Date:   May 16, 2005         /s/Jeffrey A. Rothman
                                 Jeffrey A. Rothman
                                 President,
                                 Demeter Management Corporation,
                                 general partner of the registrant